Feature detection of magnetic vortices in simulations of superconductors

In simulations of superconducting materials in the past, vortices have been visualized by examining contour plots and isosurfaces of the complex-valued order parameter field. However, these methods, primarily used for small-scale simulations, blur the fine details of the vortices, scale poorly to large-scale simulations, and do not easily enable isolating and tracking individual vortices. Here we develop a feature extraction technique for exactly finding the vortex core lines from a complex-valued order parameter field defined on a structured Cartesian finite-difference discretization mesh. With this method, the vortices can be easily described at a resolution even finer than the mesh itself. The precise determination of the vortex cores allows the interplay of the vortices inside a model superconductor to be visualized in higher resolution than has previously been possible. This feature extraction method also massively reduces the data footprint of the simulations and provides the data structures for further analysis and feature tracking. Finding the vortices in a modeled type-II superconducting material is important because the dynamics of the vortices play a critical role in determining the performance of the material.